On the exponents of primitive digraphs with the shortest elementary circuit length s (Q1105617)

Let \({\mathcal D}_ s(n)=\{D\); D is a primitive digraph on n vertices of the shortest circuit length \(s\}\), \(b_ s(n)=\max \{\gamma (D)\); \(D\in {\mathcal D}_ s(n)\}\), where \(\gamma\) (D) is the exponent of D. The authors determine the values \(b_ s(n)\) and the digraphs of \({\mathcal D}_ s(n)\) with the property \(\gamma (D)=b_ s(n)\) are characterized for \(s\geq 3\), \(s\neq 6\), and \(\gcd (s,n)>1\).